Scientist have just recently taught rats how to play hide-and-seek for fun. Other scientists have found out that slime mold will model the Japanese railroad system. I wouldn't be surprised if rodents (plural) instinctively have a go strategy once someone figures how to make an analog game for them.

its probably safe to assume that even if rodents are behaviorally trained to follow complex rules, they are mostly pattern-matching, and are lacking higher-level abstraction and communication models like humans do. If they did they would at least attempt to communicate with us, like we do with them. In such a case, an elephant that plays go by patternmatching is no different from a neural network that learned by patternmatching